On wave propagation in waveguides

Cut-off frequencies are well known in waveguides of different nature to be the thresholds of propagation and evanescence. In the present paper, a theoretical study is made to demonstrate that a combined excitation of a plane wave and waveguide mode may lead to the propagation of a nonlinear wave pattern irrespective of whether the frequency of the waveguide mode is higher or below linear cut-off. A particular problem is examined when a piston performs sinusoidal rotational vibrations combined with translational displacements in a uniform semi-infinite two-dimensional fluid duct. The frequency of the vibrations is close to a cut-off frequency. The rotational vibrations are small compared to the translational displacements. An analytical solution of the problem is obtained for uniformly accelerated piston displacements. It is shown that longitudinal plane waves guide the duct modes along the duct, such that propagation takes place even if the forcing frequencies are below linear cut-off.